A multi-D model for Raman amplification. (English) Zbl 1452.76282

Colin, Mathieu; Colin, Thierry

ESAIM, Math. Model. Numer. Anal. 45, No. 1, 1-22 (2011).

Summary: In this paper, we continue the study of the Raman amplification in plasmas that we initiated in [the authors, Differ. Integral Equ. 17, No. 3–4, 297–330 (2004; Zbl 1174.35528); J. Comput. Appl. Math. 193, No. 2, 535–562 (2006; Zbl 1092.35101)]. We point out that the Raman instability gives rise to three components. The first one is collinear to the incident laser pulse and counter propagates. In 2-D, the two other ones make a non-zero angle with the initial pulse and propagate forward. Furthermore they are symmetric with respect to the direction of propagation of the incident pulse. We construct a non-linear system taking into account all these components and perform some 2-D numerical simulations.

MSC:

76X05	Ionized gas flow in electromagnetic fields; plasmic flow
35Q55	NLS equations (nonlinear Schrödinger equations)
35Q60	PDEs in connection with optics and electromagnetic theory
78A60	Lasers, masers, optical bistability, nonlinear optics

Keywords:

Raman amplification; Zakharov system; weakly nonlinear theory